$\binom{n}{r} \div \binom{n}{n-1} = \dots$

In an apartment,there are $30$ kids. If each kid plays table tennis with every other kid exactly once,then the total number of matches played by them is:

In how many ways can $4$ balls be picked from $6$ black and $4$ green colored balls such that at least one black ball is selected?

$A$ committee of $3$ persons is to be constituted from a group of $2$ men and $3$ women. In how many ways can this be done? How many of these committees would consist of $1$ man and $2$ women?

If $^{15}C_{3r} = ^{15}C_{r+3}$,then the value of $r$ is

Out of $7$ consonants and $4$ vowels,the number of words consisting of $3$ consonants and $2$ vowels that can be formed is: